I am having same issue and it is definitely not simply a "user error" but I have some insights to share.
All permissions have been setup correctly. I have downtime scheduled, I have 1 minute time limit for all entertainment which includes YouTube. Only essential apps are in the Always Allowed list, so no YouTube or Spotify on there, yet my daughter can watch 2 hours and 40 minutes of YouTube today. It is really frustrating but I have also discovered a few things she has been doing to go around the many limits.
One method to play apple music after downtime is she uses the clock app to setup new alarms and in the alarm app you can use a song as the alarm sound. She then chooses her playlist of songs she wants and as it starts to play, she turns the screen off so the music keeps playing in apple music in the background. Then on the lock screen there comes the apple music mini player so she can skip to the next song and keep going for hours after downtime. My solution here is to block the clock app after downtime as well, so remove it from always allowed. I will wait to see if this is truly working and make an update here.
Also note, they can watch music videos in Apple music but you can also block this under the content restrictions. Its fine for me to listen to the music but spending hours watching music videos is nonsense. There are also music videos in Spotify but also strange series they can watch. I’m considering getting rid of spotify all together because I have not found settings to block these. Also, sometimes I notice youtube time being counted along with Spotify, maybe it has to do with the videos in spotify but I'm not sure yet.
For Youtube, one method is to send links to friends in iMessage. Here they can watch youtube videos directly in iMessage without using the youtube app, so no limit is ever reached. This one is solved by blocking youtube.com website. So the Youtube app still works but they can't access youtube directly from the browser. Also, never install or allow Google Chrome, it seems to also ignores the blocked sites and limits. Safari is better here of course.
The next one is she either force restarts the device or lets the battery die so it goes off. Then when she plugs it onto the charger and the device starts up again....somehow all the limits are gone until I go into screen time settings on my phone and I guess the configuration gets sent back to her device. This one is done on her iPad, not the iPhone. I have not found a way around this yet.
I'm a software engineer and this baffles me. So these bugs are obviously unique and they are also learning these from friends who have figured things out.
We can all hope our children do the right things but sadly the addiction is too strong. In the end we are responsible for them so the consequence has to be to remove the apps. If they are willingly finding ways around agreed rules then they lose these privileges. Of course I wish Apple would just fix these bugs but there are always loopholes to everything and since there is no fix in sight, I will remove the apps completely. I expect tears and random burst of anger but this is what it has come to for us.
I hope this helps another parent, particular the access to sites through the messenger. That one really irritated me because she could access Instagram and other site I had blocked.